Solve 9/1250*2*5/2:[3*3/10*(3/4-frac{1}{12})*(frac{1}{6}+frac{1}{3})]=x:[(28-6)*frac{1}{3}-(frac{43}{40}*frac{10}{3}-frac{5}{4})]

$$\frac { 9 } { 1250 } \cdot 2 \cdot \frac { 5 } { 2 } : [ 3 \cdot \frac { 3 } { 10 } \cdot ( \frac { 3 } { 4 } - \frac { 1 } { 12 } ) \cdot ( \frac { 1 } { 6 } + \frac { 1 } { 3 } ) ] = x : [ ( 28 - 6 ) \cdot \frac { 1 } { 3 } - ( \frac { 43 } { 40 } \cdot \frac { 10 } { 3 } - \frac { 5 } { 4 } ) ]$$

Solve for x

$$x=\frac{3}{5}=0.6$$

Steps for Solving Linear Equation

Express \frac{9}{1250}\times 2 as a single fraction.

$$\frac{\frac{9\times 2}{1250}\times \frac{5}{2}}{3\times \frac{3}{10}\left(\frac{3}{4}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Multiply 9 and 2 to get 18.

$$\frac{\frac{18}{1250}\times \frac{5}{2}}{3\times \frac{3}{10}\left(\frac{3}{4}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Reduce the fraction \frac{18}{1250} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{625}\times \frac{5}{2}}{3\times \frac{3}{10}\left(\frac{3}{4}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Multiply \frac{9}{625} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 5}{625\times 2}}{3\times \frac{3}{10}\left(\frac{3}{4}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Do the multiplications in the fraction \frac{9\times 5}{625\times 2}.

$$\frac{\frac{45}{1250}}{3\times \frac{3}{10}\left(\frac{3}{4}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Reduce the fraction \frac{45}{1250} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{9}{250}}{3\times \frac{3}{10}\left(\frac{3}{4}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Express 3\times \frac{3}{10} as a single fraction.

$$\frac{\frac{9}{250}}{\frac{3\times 3}{10}\left(\frac{3}{4}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{9}{250}}{\frac{9}{10}\left(\frac{3}{4}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{1}{12} to fractions with denominator 12.

$$\frac{\frac{9}{250}}{\frac{9}{10}\left(\frac{9}{12}-\frac{1}{12}\right)\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Since \frac{9}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{250}}{\frac{9}{10}\times \frac{9-1}{12}\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Subtract 1 from 9 to get 8.

$$\frac{\frac{9}{250}}{\frac{9}{10}\times \frac{8}{12}\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{9}{250}}{\frac{9}{10}\times \frac{2}{3}\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Multiply \frac{9}{10} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{250}}{\frac{9\times 2}{10\times 3}\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Do the multiplications in the fraction \frac{9\times 2}{10\times 3}.

$$\frac{\frac{9}{250}}{\frac{18}{30}\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Reduce the fraction \frac{18}{30} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{9}{250}}{\frac{3}{5}\left(\frac{1}{6}+\frac{1}{3}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{9}{250}}{\frac{3}{5}\left(\frac{1}{6}+\frac{2}{6}\right)}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Since \frac{1}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9}{250}}{\frac{3}{5}\times \frac{1+2}{6}}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Add 1 and 2 to get 3.

$$\frac{\frac{9}{250}}{\frac{3}{5}\times \frac{3}{6}}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{9}{250}}{\frac{3}{5}\times \frac{1}{2}}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Multiply \frac{3}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{250}}{\frac{3\times 1}{5\times 2}}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Do the multiplications in the fraction \frac{3\times 1}{5\times 2}.

$$\frac{\frac{9}{250}}{\frac{3}{10}}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Divide \frac{9}{250} by \frac{3}{10} by multiplying \frac{9}{250} by the reciprocal of \frac{3}{10}.

$$\frac{9}{250}\times \frac{10}{3}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Multiply \frac{9}{250} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 10}{250\times 3}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Do the multiplications in the fraction \frac{9\times 10}{250\times 3}.

$$\frac{90}{750}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Reduce the fraction \frac{90}{750} to lowest terms by extracting and canceling out 30.

$$\frac{3}{25}=\frac{x}{\left(28-6\right)\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Subtract 6 from 28 to get 22.

$$\frac{3}{25}=\frac{x}{22\times \frac{1}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Multiply 22 and \frac{1}{3} to get \frac{22}{3}.

$$\frac{3}{25}=\frac{x}{\frac{22}{3}-\left(\frac{43}{40}\times \frac{10}{3}-\frac{5}{4}\right)}$$

Multiply \frac{43}{40} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{25}=\frac{x}{\frac{22}{3}-\left(\frac{43\times 10}{40\times 3}-\frac{5}{4}\right)}$$

Do the multiplications in the fraction \frac{43\times 10}{40\times 3}.

$$\frac{3}{25}=\frac{x}{\frac{22}{3}-\left(\frac{430}{120}-\frac{5}{4}\right)}$$

Reduce the fraction \frac{430}{120} to lowest terms by extracting and canceling out 10.

$$\frac{3}{25}=\frac{x}{\frac{22}{3}-\left(\frac{43}{12}-\frac{5}{4}\right)}$$

Least common multiple of 12 and 4 is 12. Convert \frac{43}{12} and \frac{5}{4} to fractions with denominator 12.

$$\frac{3}{25}=\frac{x}{\frac{22}{3}-\left(\frac{43}{12}-\frac{15}{12}\right)}$$

Since \frac{43}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{25}=\frac{x}{\frac{22}{3}-\frac{43-15}{12}}$$

Subtract 15 from 43 to get 28.

$$\frac{3}{25}=\frac{x}{\frac{22}{3}-\frac{28}{12}}$$

Reduce the fraction \frac{28}{12} to lowest terms by extracting and canceling out 4.

$$\frac{3}{25}=\frac{x}{\frac{22}{3}-\frac{7}{3}}$$

Since \frac{22}{3} and \frac{7}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{25}=\frac{x}{\frac{22-7}{3}}$$

Subtract 7 from 22 to get 15.

$$\frac{3}{25}=\frac{x}{\frac{15}{3}}$$

Divide 15 by 3 to get 5.

$$\frac{3}{25}=\frac{x}{5}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x}{5}=\frac{3}{25}$$

Multiply both sides by 5.

$$x=\frac{3}{25}\times 5$$

Express \frac{3}{25}\times 5 as a single fraction.

$$x=\frac{3\times 5}{25}$$

Multiply 3 and 5 to get 15.

$$x=\frac{15}{25}$$

Reduce the fraction \frac{15}{25} to lowest terms by extracting and canceling out 5.

$$x=\frac{3}{5}$$